Question: Simplify the following expression: $r = \dfrac{n^2 + 10n + 21}{n + 3} $
Explanation: First factor the polynomial in the numerator. $ n^2 + 10n + 21 = (n + 3)(n + 7) $ So we can rewrite the expression as: $r = \dfrac{(n + 3)(n + 7)}{n + 3} $ We can divide the numerator and denominator by $(n + 3)$ on condition that $n \neq -3$ Therefore $r = n + 7; n \neq -3$